Processes for the electrochemical processing of a component with at least one electrode have been known. For example, the so-called electrochemical sinking process is an example of a process to exactly and highly precisely finish surfaces. In electrochemical sinking, the surface of the component is processed, as a rule, with at least one electrode, with a removal of material occurring to the component due to an electrochemical reaction of the component with the electrolyte located between the component and the electrode. However, a disadvantage of the known electrochemical sinking processes is that, for example, in the sinking of components of a gas turbine or of a low or high pressure compressor, finished partial component surfaces that already have the required final contours are corroded by the electrochemical process and are partially eroded. The erosion leads to an undesirable change of the geometry, to the effect that, as a rule, blueprint tolerances are exceeded. Such inaccuracies are undesirable, particularly in turbine engineering. In particular, they prevent any further automatization in the production process of the aforementioned components from being achieved.